Average Error: 2.9 → 0.0
Time: 9.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}
double f(double x, double y, double z) {
        double r374486 = x;
        double r374487 = y;
        double r374488 = 1.1283791670955126;
        double r374489 = z;
        double r374490 = exp(r374489);
        double r374491 = r374488 * r374490;
        double r374492 = r374486 * r374487;
        double r374493 = r374491 - r374492;
        double r374494 = r374487 / r374493;
        double r374495 = r374486 + r374494;
        return r374495;
}
↓
double f(double x, double y, double z) {
        double r374496 = x;
        double r374497 = 1.0;
        double r374498 = z;
        double r374499 = exp(r374498);
        double r374500 = 1.1283791670955126;
        double r374501 = r374499 * r374500;
        double r374502 = y;
        double r374503 = r374501 / r374502;
        double r374504 = r374503 - r374496;
        double r374505 = r374497 / r374504;
        double r374506 = r374496 + r374505;
        return r374506;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.9

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]

  4. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - \frac{x}{1}}}\]

  5. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{e^{z} \cdot 1.128379167095512558560699289955664426088}{y} - x}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))